A note on epidemics in heterogeneous populations

Recent analysis has shown the importance of heterogeneity for understanding the course of epidemics. However, the results generally rely on computer models or the assumption that the population consists of internally homogeneous subgroups. This note presents some analytic results for the more general case, in which any distribution can characterize population heterogeneity in susceptibility under proportionate mixing. At any moment, epidemics in such a situation resemble classic epidemics, with rate of spread governed by the average susceptibility of those not yet infected. But, over time, this average susceptibility falls at a rate proportional to the dispersion of susceptibility among those not yet infected. The author concludes by noting some implications of heterogeneity for understanding epidemics.